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Generalized Bernoulli process: simulation, estimation, and application

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  • Lee Jeonghwa

    (Department of Statistics, Truman State University, USA)

Abstract

A generalized Bernoulli process (GBP) is a stationary process consisting of binary variables that can capture long-memory property. In this paper, we propose a simulation method for a sample path of GBP and an estimation method for the parameters in GBP. Method of moments estimation and maximum likelihood estimation are compared through empirical results from simulation. Application of GBP in earthquake data during the years of 1800-2020 in the region of conterminous U.S. is provided.

Suggested Citation

  • Lee Jeonghwa, 2021. "Generalized Bernoulli process: simulation, estimation, and application," Dependence Modeling, De Gruyter, vol. 9(1), pages 141-155, January.
    • Handle: RePEc:vrs:demode:v:9:y:2021:i:1:p:141-155:n:7
    DOI: 10.1515/demo-2021-0106
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    References listed on IDEAS

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    1. Delgado, Rosario, 2007. "A reflected fBm limit for fluid models with ON/OFF sources under heavy traffic," Stochastic Processes and their Applications, Elsevier, vol. 117(2), pages 188-201, February.
    2. Jean-Christophe Breton & Jean-François Coeurjolly, 2012. "Confidence intervals for the Hurst parameter of a fractional Brownian motion based on finite sample size," Statistical Inference for Stochastic Processes, Springer, vol. 15(1), pages 1-26, April.
    3. Jean-François Coeurjolly, 2001. "Estimating the Parameters of a Fractional Brownian Motion by Discrete Variations of its Sample Paths," Statistical Inference for Stochastic Processes, Springer, vol. 4(2), pages 199-227, May.
    4. Beghin, L., 2012. "Random-time processes governed by differential equations of fractional distributed order," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1314-1327.
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